J-PARC hadron physics in 2016 Open en char arm production duction in exclusive e rea eact ctions ions at t PANDA-FAI AIR R an and J-PAR ARC C en ener ergy gy region ion Alexander Titov Bogoliubov Lab. of Theoretical Physics, JINR Dubna, Russia and RCNP, Osaka University, Japan Helmholtz Zentrum-Dresden-Rossendorf, Germany and Atsushi Hosaka RCNP, Osaka University, Japan/KEK 1 “J - PARC hadron physics in 2016”
The aim of our discussion is qualitative/quantitative estimation of open charm production in reactions with one flavor exchange (PANDA) and reactions with two flavor exchange open charm production in reactions (J-PARC) also in reactions, like mainly in forward production (large ) 2 “J - PARC hadron physics in 2016”
Charmed and strange hadrons 3 “J - PARC hadron physics in 2016”
Challenges of some utilized models 4 “J - PARC hadron physics in 2016”
Open charm at high energy and pQCD models M. Basile et al ., Lett. Nuovo Cim. 30, 487 (1981) “ Intrinsic charm model ” Brodsky et al , PLB 93 (1980) 1 5 “J - PARC hadron physics in 2016”
Heidenbauer, Krein et al., (1993-2015) Effective Lagrangian Models Shyam&Lenske,(2015) Example: A. Eide et al ., Nucl. Phys. B 60,173 (1973) (LEAR) Definite enhancement at forward production angles encourage for t-exchange channels 6 “J - PARC hadron physics in 2016”
Amplitude and cross sections 7 “J - PARC hadron physics in 2016”
Kinematics: momentum transfers 8 “J - PARC hadron physics in 2016”
Limited region of application experiment experiment Wrong energy dependence 9 “J - PARC hadron physics in 2016”
Contrary to the hadron-exchange models,Regge approaches are work satisfactorily for strangeness production Similarity of and motivates for utilizing the Regge models for charm production internal lines are associated with Regge trajectories 5 2 3 4 1 linear trajectories small yields of charm Therefore, there are doubts: non-linear? Chew-Frautschi plot 10 “J - PARC hadron physics in 2016”
V. Barger, R.Phillips, PRD 12 (1975) 11 “J - PARC hadron physics in 2016”
Possible solution is an approach based on non-perturbative quark-gluon string model discussed for the firrst time by S.Nussinov , ( PRL 34 (1975) and F.Low , PRD 12 (1975)) Essentially, they discussed formation and decay of a color tube with complicated intermediate (multi-particle) states The method of evaluation of observables based on utilizing the planar diagram for two body amplitude and it’s cutting In s -channel was elaborated by Kaidalov (almost 10 years later ) [Z.Phys. C 12 (1982)] and developed by Kaidalov et al. (in 1983-2005 ) and other groups: A.T., Kampfer(2008), A.Khojiamirian et al.(2012), G.Lykasov et al .(2010)… V. Grishina et al.(2005)(strangeness), Kim, Hosaka & et al ., (2015) …. … 12 ( In particularly for two-body exclusive processes!!) “J - PARC hadron physics in 2016”
required looks like “Regge trajectory” with an effective “ij” Reggeon diagram (amplitude) 13 “J - PARC hadron physics in 2016”
The main advantage of Kaidalov’s approach based on factorization: (i) Regge type of the individual and the “required amplitude”: (ii) A.Kaidalov, is a derivation of the consistent equations for Z.Phys.C12, 62 (1982) (1) and (2) (3) with 14 “J - PARC hadron physics in 2016”
Example: 15 “J - PARC hadron physics in 2016”
Non-linear trajectory reflects behavior of QCD motivated potential frequency total string length string tension string spin momentum string energy 16 “J - PARC hadron physics in 2016”
Non-linear Regge trajectories for diagonal channels in a square root form Brisudova, Burakovsky, and Goldman PRD 61 , (2000). non-linear linear universal value are taken as input 17 “J - PARC hadron physics in 2016”
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unknown residual function Stoks & Rijken PRC, 59 , 3009 (‘99) important note: for unpolarized case 19 “J - PARC hadron physics in 2016”
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t - dependence 21 “J - PARC hadron physics in 2016”
energy dependence 22 “J - PARC hadron physics in 2016”
Comparison of two realization of QGSM for A.Khodjamirian,C. Klein, T.Mannel and Y.-M. Wang Phys. Rev. C78,025291 (2008) Eur.Phys.J.A.48,31(2012) C(0) 5…8 C(t) the uncertainties caused the uncertainties caused by LCSR of strong couplings by the residual function C(t) 23 “J - PARC hadron physics in 2016”
Comparison of two realization of QGSM (average values) A.Khodjamirian,C. Klein, T.Mannael and Y.-M. Wang Phys. Rev. C78,025291 (2008) Eur.Phys.J.A.48,31(2012) av. (AT) av. (AK) the uncertainties caused the uncertainties caused by LCSR of strong couplings by the residual function C(t) for the average values both predictions are consistent with each other 24 within a factor of 2 “J - PARC hadron physics in 2016”
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d-diquark 26 “J - PARC hadron physics in 2016”
How to evaluate the di-quark trajectory? is taken as input [cf. K.Storrow Phys. Rep. 103,135(1984)] then and allows to identify trajectory of 27 “J - PARC hadron physics in 2016”
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t-dependence - + 29 “J - PARC hadron physics in 2016”
s-dependence 30 “J - PARC hadron physics in 2016”
Comparison of two realization of QGSM for Phys. Rev. C78,025291 (2008) Eur. Phys. J.A48, 31(2012) 31 “J - PARC hadron physics in 2016”
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Double flavor exchange: and in collisions Cut (pole) diagrams Cutkosky cutting rule 33 “J - PARC hadron physics in 2016”
The vertex amplitudes: “effective region exchange” 34 “J - PARC hadron physics in 2016”
transition is a coherent sum with The amplitude of intermediate states SU(3) predicts coupling constant independent amplitude for one has the ratio of cross sections looks as 35 “J - PARC hadron physics in 2016”
Cross sections differential total 36 “J - PARC hadron physics in 2016”
reactions Exclusive 37 “J - PARC hadron physics in 2016”
Differential cross sections Total cross sections [cf. K. Boreskov, A.Kaidalov, Sov.J. Nucl.Phys. 37 (1982)] vs. [cf. V. Barger, R.Phillips, PRD 12 (1975)] 38 “J - PARC hadron physics in 2016”
For high energy cf. K. Boreskov, A.Kaidalov, Sov.J. Nucl.Phys. 37 (1982) For J-PARC energies our work is in a progress 39 “J - PARC hadron physics in 2016”
Summary We have evaluated the cross sections for reactions, including double flavor exchange, and for reactions at ambiguity with residual function!! This result may be used for design of PANDA detector and “charm” program at JPARC And for further development of the theoretical approaches in “charmed physics” 40 “J - PARC hadron physics in 2016”
Thank you very much for attention ! 41 “J - PARC hadron physics in 2016”
BACKUP 42 “J - PARC hadron physics in 2016”
Longitudinal asymmetries where Polarized Antiproton EXperiment (PAX) 43 “J - PARC hadron physics in 2016”
spin-conserving spin-flip spin-conserving 44 “J - PARC hadron physics in 2016”
Structure of spin-flip amplitude 45 “J - PARC hadron physics in 2016”
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Asymmetry s-dependence 47 “J - PARC hadron physics in 2016”
0 48 “J - PARC hadron physics in 2016”
Asymmetry t-dependence 49 “J - PARC hadron physics in 2016”
Asymmetry s-dependence 50 “J - PARC hadron physics in 2016”
pure vector coupling!!! 51 “J - PARC hadron physics in 2016”
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J.Haindenbauer and J.Krein OBE model Phys. Lett. B 687 (2010) 55 “J - PARC hadron physics in 2016”
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